报告题目：High-dimensional Quantile Tensor Regression

演讲人：朱仲义复旦大学教授，博士生导师

报告时间：2021年4月9日（周五）14:00-15:30

报告地点：经济管理学院335

摘要：Quantile regression is an indispensable tool for statisticallearning. Traditional  quantile regression methods consider vector-valuedcovariates and estimate the corresponding coefficient vector. Many modernapplications involve data with a tensor structure. In this paper, we propose aquantile regression model which takes tensors as covariates, and present anestimation approach based on Tucker decomposition. It effectively reduces thenumber of parameters, leading to efficient estimation and feasible computation. We also use a sparse Tucker decomposition, which is a popular approach in theliterature, to further reduce the number of parameters when the dimension ofthe tensor is large. We propose an alternating update algorithm combined withalternating direction method of multipliers (ADMM). The asymptotic propertiesof the estimators are established under suitable conditions. The numericalperformances are demonstrated via simulations and an application to a crowddensity estimation problem.

演讲人简介：朱仲义教授是复旦大学管理学院统计系教授，博士生导师；曾任中国概率统计学会第八、九届副理事长,国际著名杂志”Statistica Sinica”副主编; “应用概率统计”, “数理统计与管理”杂志编委，中国统计教材编审委员会委员；现为Elected Member of the ISI（国际数理统计学会）；  ”中国科学：数学”杂志编委。专业研究方向为：保险精算；纵向数据(面板数据)模型；分位数回归模型等。主持完成国家自然科学基金四项、国家社会科学基金一项，作为子项目负责人完成国家自然科学基金重点项目一项。目前主持国家自然科学基金重大项目子项目一项，重点项目子项目一项，面上项目一项。近几年发表论文100多篇(其中包括在国际顶级刊物：J.R.Stat.Soc B, J.A.S.A., Ann. Statist. 和Biometrika等SCI论文五十多篇) 。第一完成人获得教育部自然科学二等奖一次。